The rule means that when a creature is tapped it loses 2k power. When it isn't tapped it doesn't lose that power. Battles happen after a creature is tapped, anything with 2k power or less will die before the battle takes place.

It's also a permanent effect for as long as it's in the battle zone and the effect stacks as far as I'm aware. If you have two Necrodragon Zanjibar in play your opponents tapped creatures lose 4k.